Question

\(2x^2+12y^2-8x-12y+11=0\)

vậy xy=..........

Answer 1

\(2x^2+12y^2-8x-12y+11=0\)

\(\Rightarrow\left(2x^2-8x+8\right)+\left(12y^2-12y+3\right)=0\)

\(\Rightarrow2\left(x^2-4x+4\right)+3\left(12y^2-12y+3\right)=0\)

\(\Rightarrow2\left(x-2\right)^2+3\left(2y-1\right)^2=0\)

\(\Rightarrow\left\{\begin{matrix}2\left(x-2\right)^2=0\\3\left(2y-1\right)^2=0\end{matrix}\right.\)\(\Rightarrow\left\{\begin{matrix}x-2=0\\2y-1=0\end{matrix}\right.\)\(\Rightarrow\left\{\begin{matrix}x=2\\y=\frac{1}{2}\end{matrix}\right.\)

Khi đó \(xy=2\cdot\frac{1}{2}=1\)